A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes at steady state when it flows through a microfluidic microchannel of comparable cross-sectional size. From the mid-plane capsule profile, we deduce two characteristic geometric quantities that uniquely characterize the shape taken by the microcapsule under external hydrodynamic stresses. To identify the values of the unknown rigidity of the membrane and of the size of the capsule, we compare the geometric quantities with the values predicted numerically using a fluid-structure-interaction model by solving the three-dimensional capsule-flow interactions. The complete numerical data set is obtained off-line by systematically varying the governing parameters of the problem, i.e. the capsule-to-tube confinement ratio, and the capillary number, which is the ratio of the viscous to elastic forces. We show that diffuse approximation efficiently estimates the unknown mechanical resistance of the capsule membrane. We validate the data-driven procedure by applying it to the geometric and mechanical characterization of ovalbumin microcapsules (diameter of the order of a few tens of microns). As soon as the capsule is sufficiently deformed to exhibit a parachute shape at the rear, the capsule size and surface shear modulus are determined with an accuracy of 0.2% and 2.7%, respectively, as compared with 2–3% and 25% without it, in the best cases (Hu et al. Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law. Phys Rev E 2013; 87(6): 063008). Diffuse approximation thus allows the capsule size and membrane elastic resistance to be provided quasi-instantly with very high precision. This opens interesting perspectives for industrial applications that require tight control of the capsule mechanical properties in order to secure their behavior when they transport active material.

提出了一种基于扩散近似的新型数据驱动的实时程序，以从其变形形状表征液核微胶囊的机械性能，并通过逆分析确定保护内核的亚微米级膜的机械性能。该方法首先涉及通过实验获得给定微胶囊流经横截面尺寸可比较的微流体微通道时在稳态下呈现的变形形状。从中平面胶囊的轮廓，我们推导出两个特征性的几何量，它们独特地表征了微胶囊在外部水动力应力作用下的形状。为了确定未知的膜片刚度和胶囊大小的值，我们通过解决三维胶囊-流动相互作用，将几何量与使用流体-结构-相互作用模型数值预测的值进行比较。脱机获得完整的数值数据集是通过系统地改变问题的控制参数，即胶囊对管子的约束比和毛细管数，即粘滞力与弹性力的比。我们表明，扩散近似有效地估计了未知的胶囊膜的机械阻力。我们通过将其应用于卵清蛋白微胶囊的几何和机械表征（直径为几十微米的量级）来验证数据驱动程序。一旦胶囊充分变形以在后方呈现降落伞形状，Phys Rev E 2013；87（6）：063008）。因此，漫反射近似可以非常高精度地准时提供胶囊的尺寸和膜的弹性阻力。这为需要严格控制胶囊机械性能以确保其在运输活性材料时的行为的工业应用打开了有趣的前景。